1. Field of the Invention
The present invention relates to an image-forming method and an image-forming apparatus. More particularly, the present invention relates to an image-forming method that uses a microscope. The present invention also relates to an image-forming apparatus using a microscope.
2. Description of Related Art
In image formation by an image-forming optical system, e.g. an optical microscope, a transfer function unique to each particular image-forming optical system exists as detailed in J. W. Goodman, "Introduction to Fourier Optics", McGraw-Hill (1968) by way of example. The characteristics of an object image formed by an image-forming optical system is limited by the transfer function. More specifically, among Fourier components (spatial frequency components) of an optical image to be transferred by an image-forming optical system, only those in a specific spatial frequency region determined by the transfer function of the image-forming optical system are transferred, and the remaining spatial frequency components are cut off.
For example, in an ordinary optical microscope, a spatial frequency f.sub.cutoff exists, which is determined by the numerical aperture (NA) of the objective and known as "cutoff frequency": EQU f.sub.cutoff =2NA/.lambda. (1)
(where .lambda. is the wavelength of light)
Among the Fourier components of an input optical image, spatial frequency components higher than the cutoff frequency are cut off and hence cannot be reflected in image formation.
As shown in FIG. 12 in the accompanying drawings, the numerical aperture of an objective 1 is determined by multiplying together the sine function of 1/2 of the apex angle of the cone of light 2 that the objective 1 can take in from an observation object O and the refractive index of the medium between the observation object O and the front surface of the objective 1. For an object in the air, for example, the numerical aperture does not become more than 1. Therefore, the cutoff frequency does not become more than 2/.lambda.. Accordingly, ordinary optical microscopes cannot resolve a fine structure with a period smaller than 1/2 of the wavelength of light that is placed in the air.
However, spatial frequency components of an observation image in a spatial frequency region that cannot be transferred by an image-forming optical system can be reflected in image formation by inserting a spatial frequency-modulating device between the observation object and the image-forming optical system. In this case, however, the observation object image formed by the image-forming optical system has been modulated. Therefore, a correct observation object image is formed by jointly using a device for restoring the modulated image (i.e. a demodulating device). Application of this technique to an optical microscope makes it possible to resolve a fine structure of an observation object having a spatial frequency higher than the conventional cutoff frequency. This is referred to as "superresolution".
W. Lukosz, "Optical systems with resolving powers exceeding the classical limit. II", Journal of the Optical Society of America, Vol. 57, No. 7 (1967), pp. 932-941, discloses a method of obtaining superresolution by using a system arranged as shown in FIG. 19. That is, diffraction gratings 5 and 6 having conjugate grating constants are placed at respective positions conjugate to each other. More specifically, the diffraction grating 5 is placed at a position between an observation object O and an image-forming optical system 3 and near the observation object O. The diffraction grating 6 is placed behind a position where an image of the observation object O is formed by the image-forming optical system 3. With this arrangement, the diffraction gratings 5 and 6 are moved conjugably to thereby obtain superresolution. The diffraction grating 5, which is placed near the observation object O, diffracts and thus modulates light emanating from the observation object O. The light emanating from the observation object O includes spatial frequency components having angles at which they cannot enter the image-forming optical system 3. A part of such spatial frequency components are allowed to enter the image-forming optical system 3 by the modulation effected by the diffraction grating 5. That is, the propagation angle of a part of the spatial frequency components is changed by the diffraction, and the modulated components enter the image-forming optical system 3. The diffraction grating 5 produces a plurality of diffracted light beams. Therefore, an input image having a plurality of modulation components is transferred by the image-forming optical system 3, and a modulated image 4 is formed at the image-formation position of the image-forming optical system 3. The diffraction grating 6, which is placed behind the image-formation position demodulates the modulated image 4. More specifically, each modulation component having a propagation angle changed by the diffraction grating 5 near the observation object O is transferred by the image-forming optical system 3 and then passed through the diffraction grating 6, thereby restoring the changed propagation angle to the original state to form a restored image. Thus, spatial frequency components that cannot be transferred by only the image-forming optical system 3 can also be reflected in image formation by combining the image-forming optical system 3 with the diffraction gratings 5 and 6, and superresolution can be attained. However, W. Lukosz admits in the paper that it is not easy to realize such an arrangement and drive of diffraction gratings.
On the other hand, D. Mendlovic et. al., "One-dimensional superresolution optical system for temporally restricted objects", Applied Optics, Vol. 36, No. 11 (1997), pp. 2353-2359, discloses that they were successful in an experiment designed to obtain superresolution with a single rotary diffraction grating 7, as shown in FIG. 20, by using an arrangement in which an observation object O and a modulated image 4 of the observation object O, which is formed by an image-forming optical system 3, are placed in approximately the same plane. However, in such an arrangement, the magnification of the image of the observation object O formed by the image-forming optical system 3 is substantially limited to -1.
FIG. 21 shows the arrangement of a novel optical system presented by Dr. Tony Wilson (University of Oxford, Oxford, UK) at the 20th Lecture Meeting of the Society for the Research of Laser Microscopes held on Nov. 7, 1997. The optical system includes a movable diffraction grating 8, an illuminating optical system 9 that projects an image of the diffraction grating 8 on the focal position of an objective 1, an image-forming optical system 3 that forms an enlarged image of an observation object O, a CCD 10 that detects the image of the observation object O formed by the image-forming optical system 3, an image storage unit 11 that stores the image detected by the CCD 10, an arithmetic unit 12 that performs an arithmetic operation using the image stored in the image storage unit 11, and an image display unit 13 that displays the result of the arithmetic operation performed by the arithmetic unit 12. A combination of the diffraction grating 8 and the illuminating optical system 9 illuminates the observation object O with illuminating light having a sinusoidal intensity distribution. Three images of the observation object O are detected by the CCD 10 in respective states where the spatial phases of the sine wave of the illuminating light on the observation object O are different from each other by 120 degrees. From the intensity distributions I.sub.1, I.sub.2 and I.sub.3 of the three images detected by the CCD 10, a light-cut image I.sub.c is obtained by calculating the following equation: EQU I.sub.c = {(I.sub.2 -I.sub.1).sup.2 +(I.sub.3 -I.sub.2).sup.2 +(I.sub.1 -I.sub.3).sup.2 } (2)
When the observation object O is at the in-focus position of the objective 1, it is illuminated with sinusoidal illuminating light of strong contrast. Therefore, a difference is produced between the intensities I.sub.1, I.sub.2 and I.sub.3 of the three images, and I.sub.c assumes a finite value according to the characteristics of the sample. On the other hand, when the observation object O is off the in-focus position of the objective 1, the observation object O is illuminated with illuminating light having almost no contrast. Therefore, there is no difference between the intensities I.sub.1, I.sub.2 and I.sub.3 of the three images, and I.sub.c is almost zero. Consequently, only an image near the in-focus plane of the objective 1 is obtained. Thus, a light-cut image is obtained as in the case of a confocal image obtained by a conventional confocal microscopy using a pinhole. Therefore, this method will be hereinafter referred to as "fringe projection light-cut microscopy". The conventional confocal microscopy requires a high-intensity light source, e.g. an ultra high-pressure mercury lamp, whereas the fringe projection light-cut microscopy can use a low-intensity light source, e.g. a halogen lamp, and does not require a scanning optical system as needed in the conventional confocal microscopy. Accordingly, fringe projection light-cut microscopy has an advantage over conventional confocal microscopy in that it can be realized by a simple and low-cost system.
If the above-described methods proposed by W. Lukosz and D. Mendlovic, et al. are applied to an optical microscope, the following problems arise: With the method proposed by W. Lukosz, superresolution is obtained by synchronously moving the diffraction gratings 5 and 6, which are placed near the observation object O and the object image, respectively. In the case of a microscope, however, a magnifying power is introduced into the image formation. Therefore, the diffraction gratings 5 and 6, which have different grating constants, must be moved conjugably at respective positions while maintaining the conjugate relation therebetween. This is very difficult to realize. The method proposed by D. Mendlovic et al. cannot be implemented in an optical microscope in which a magnifying power other than +1 is introduced.
If it is intended to perform real-time observation with the fringe projection light-cut microscopy proposed by Dr. Tony Wilson, the following problems arise: Because equation (2) includes three squaring computations and one square root computation, a great deal of time is needed to calculate equation (2). Therefore, real-time observation cannot be performed. In addition, the light-cut image IC obtained by using equation (2) contains nonlinear components with respect to the intensities I.sub.1, I.sub.2 and I.sub.3 of the image obtained by directly imaging the observation object O. Therefore, the light-cut image IC appears unnatural.